2.53: Normal to a square-root curve and shaded area

0606/22/O/N/18 — Question 9 · 9 marks

2.53 diagram
The diagram shows part of the curve y=2xy = 2\sqrt{x}. The normal to the curve at the point A(4,4)A(4, 4) meets the xx-axis at the point BB.
(i)
Find the equation of the line ABAB.
[4]
(ii)
Find the coordinates of BB.
[1]
(iii)
Showing all your working, find the area of the shaded region.
[4]